You may have wondered what Euler's Identity means
[tex]e^{i \pi} = -1[/tex]
I hate to break it to you but it just means
[tex]\cos \pi + i \sin \pi = -1 + 0i[/tex]
Equating respective real and imaginary parts,
[tex]\cos \pi = -1, \qquad \sin \pi = 0[/tex]
which you probably already knew.
From the first part,
[tex]\pi = \arccos(-1)[/tex]
That's in the principal value range of cosine.
[tex]\pi = \textrm{Arccos}(-1)[/tex]
Answer: π
